Abstract
For a field F, let Gn(F) = {{a,Φn(a)} ∈ K2(F) | a,Φn(a) ∈ F*}, where Φn(x) is the n-th cyclotomic polynomial. At first, by using Faltings’ theorem on Mordell conjecture it is proved that if F is a number field and if n ≠ 4, 8, 12 is a positive integer having a square factor then Gn(F) is not a subgroup of K2(F), and then by using the results of Manin, Grauert, Samuel and Li on Mordell conjecture theorem for function fields, a similar result is established for function fields over an algebraically closed field.
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